Advanced Statistics: QI Portfolio I
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.014 | ||||
| SD | 0.210 | ||||
| Sharpe ratio (Glass type estimate) | -0.068 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.066 | ||||
| df | 37.000 | ||||
| t | -0.120 | ||||
| p | 0.548 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.169 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.034 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.168 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.035 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.114 | ||||
| Upside Potential Ratio | 1.214 | ||||
| Upside part of mean | 0.152 | ||||
| Downside part of mean | -0.166 | ||||
| Upside SD | 0.166 | ||||
| Downside SD | 0.125 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.505 | ||||
| Mean of criterion | -0.014 | ||||
| SD of predictor | 0.273 | ||||
| SD of criterion | 0.210 | ||||
| Covariance | -0.007 | ||||
| r | -0.127 | ||||
| b (slope, estimate of beta) | -0.098 | ||||
| a (intercept, estimate of alpha) | 0.035 | ||||
| Mean Square Error | 0.045 | ||||
| DF error | 36.000 | ||||
| t(b) | -0.767 | ||||
| p(b) | 0.776 | ||||
| t(a) | 0.260 | ||||
| p(a) | 0.398 | ||||
| Lowerbound of 95% confidence interval for beta | -0.357 | ||||
| Upperbound of 95% confidence interval for beta | 0.161 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.239 | ||||
| Upperbound of 95% confidence interval for alpha | 0.309 | ||||
| Treynor index (mean / b) | 0.145 | ||||
| Jensen alpha (a) | 0.035 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.035 | ||||
| SD | 0.202 | ||||
| Sharpe ratio (Glass type estimate) | -0.171 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.167 | ||||
| df | 37.000 | ||||
| t | -0.304 | ||||
| p | 0.618 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.272 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.933 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.269 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.935 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.258 | ||||
| Upside Potential Ratio | 1.043 | ||||
| Upside part of mean | 0.140 | ||||
| Downside part of mean | -0.174 | ||||
| Upside SD | 0.149 | ||||
| Downside SD | 0.134 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.461 | ||||
| Mean of criterion | -0.035 | ||||
| SD of predictor | 0.252 | ||||
| SD of criterion | 0.202 | ||||
| Covariance | -0.006 | ||||
| r | -0.122 | ||||
| b (slope, estimate of beta) | -0.098 | ||||
| a (intercept, estimate of alpha) | 0.011 | ||||
| Mean Square Error | 0.042 | ||||
| DF error | 36.000 | ||||
| t(b) | -0.740 | ||||
| p(b) | 0.768 | ||||
| t(a) | 0.083 | ||||
| p(a) | 0.467 | ||||
| Lowerbound of 95% confidence interval for beta | -0.368 | ||||
| Upperbound of 95% confidence interval for beta | 0.171 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.253 | ||||
| Upperbound of 95% confidence interval for alpha | 0.274 | ||||
| Treynor index (mean / b) | 0.351 | ||||
| Jensen alpha (a) | 0.011 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.094 | ||||
| Expected Shortfall on VaR | 0.116 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.042 | ||||
| Expected Shortfall on VaR | 0.085 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 38.000 | ||||
| Minimum | 0.848 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.266 | ||||
| Mean of quarter 1 | 0.959 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.051 | ||||
| Inter Quartile Range | 0.002 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.132 | ||||
| Mean of outliers low | 0.922 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.211 | ||||
| Mean of outliers high | 1.064 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.593 | ||||
| VaR(95%) (moments method) | 0.034 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.417 | ||||
| VaR(95%) (regression method) | 0.032 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.330 | ||||
| Quartile 1 | 0.330 | ||||
| Median | 0.330 | ||||
| Quartile 3 | 0.330 | ||||
| Maximum | 0.330 | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.010 | ||||
| Compounded annual return (geometric extrapolation) | 0.010 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.029 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.082 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.016 | ||||
| SD | 0.193 | ||||
| Sharpe ratio (Glass type estimate) | -0.085 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.085 | ||||
| df | 832.000 | ||||
| t | -0.152 | ||||
| p | 0.560 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.185 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.014 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.185 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.014 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.135 | ||||
| Upside Potential Ratio | 3.804 | ||||
| Upside part of mean | 0.463 | ||||
| Downside part of mean | -0.480 | ||||
| Upside SD | 0.150 | ||||
| Downside SD | 0.122 | ||||
| N nonnegative terms | 175.000 | ||||
| N negative terms | 658.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 833.000 | ||||
| Mean of predictor | 0.530 | ||||
| Mean of criterion | -0.016 | ||||
| SD of predictor | 0.321 | ||||
| SD of criterion | 0.193 | ||||
| Covariance | -0.002 | ||||
| r | -0.026 | ||||
| b (slope, estimate of beta) | -0.015 | ||||
| a (intercept, estimate of alpha) | -0.008 | ||||
| Mean Square Error | 0.037 | ||||
| DF error | 831.000 | ||||
| t(b) | -0.740 | ||||
| p(b) | 0.770 | ||||
| t(a) | -0.076 | ||||
| p(a) | 0.530 | ||||
| Lowerbound of 95% confidence interval for beta | -0.056 | ||||
| Upperbound of 95% confidence interval for beta | 0.026 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.222 | ||||
| Upperbound of 95% confidence interval for alpha | 0.205 | ||||
| Treynor index (mean / b) | 1.069 | ||||
| Jensen alpha (a) | -0.008 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.035 | ||||
| SD | 0.189 | ||||
| Sharpe ratio (Glass type estimate) | -0.183 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.183 | ||||
| df | 832.000 | ||||
| t | -0.326 | ||||
| p | 0.628 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.282 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.916 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.282 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.917 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.275 | ||||
| Upside Potential Ratio | 3.599 | ||||
| Upside part of mean | 0.453 | ||||
| Downside part of mean | -0.487 | ||||
| Upside SD | 0.141 | ||||
| Downside SD | 0.126 | ||||
| N nonnegative terms | 175.000 | ||||
| N negative terms | 658.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 833.000 | ||||
| Mean of predictor | 0.478 | ||||
| Mean of criterion | -0.035 | ||||
| SD of predictor | 0.324 | ||||
| SD of criterion | 0.189 | ||||
| Covariance | -0.002 | ||||
| r | -0.026 | ||||
| b (slope, estimate of beta) | -0.015 | ||||
| a (intercept, estimate of alpha) | -0.027 | ||||
| Mean Square Error | 0.036 | ||||
| DF error | 831.000 | ||||
| t(b) | -0.742 | ||||
| p(b) | 0.771 | ||||
| t(a) | -0.257 | ||||
| p(a) | 0.601 | ||||
| Lowerbound of 95% confidence interval for beta | -0.055 | ||||
| Upperbound of 95% confidence interval for beta | 0.025 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.237 | ||||
| Upperbound of 95% confidence interval for alpha | 0.182 | ||||
| Treynor index (mean / b) | 2.304 | ||||
| Jensen alpha (a) | -0.027 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 833.000 | ||||
| Minimum | 0.879 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.195 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 183.000 | ||||
| Percentage of outliers low | 0.220 | ||||
| Mean of outliers low | 0.992 | ||||
| Number of outliers high | 178.000 | ||||
| Percentage of outliers high | 0.214 | ||||
| Mean of outliers high | 1.008 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.177 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.645 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | 0.021 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.006 | ||||
| Quartile 3 | 0.010 | ||||
| Maximum | 0.399 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.004 | ||||
| Mean of quarter 3 | 0.008 | ||||
| Mean of quarter 4 | 0.207 | ||||
| Inter Quartile Range | 0.007 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.125 | ||||
| Mean of outliers high | 0.399 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.010 | ||||
| Compounded annual return (geometric extrapolation) | 0.009 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.024 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.046 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.396 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | NA | ||||
| Sharpe ratio (Hedges UMVUE) | NA | ||||
| df | NA | ||||
| t | NA | ||||
| p | NA | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.176 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.513 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | NA | ||||
| b (slope, estimate of beta) | NA | ||||
| a (intercept, estimate of alpha) | NA | ||||
| Mean Square Error | NA | ||||
| DF error | NA | ||||
| t(b) | NA | ||||
| p(b) | NA | ||||
| t(a) | NA | ||||
| p(a) | NA | ||||
| Lowerbound of 95% confidence interval for beta | NA | ||||
| Upperbound of 95% confidence interval for beta | NA | ||||
| Lowerbound of 95% confidence interval for alpha | NA | ||||
| Upperbound of 95% confidence interval for alpha | NA | ||||
| Treynor index (mean / b) | NA | ||||
| Jensen alpha (a) | NA | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -12492933348697024.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -12420719861132300.000 | ||||
| df | 130.000 | ||||
| t | -8833837887775228.000 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13930479873814932.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10910959848449668.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.041 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.517 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | 0.000 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -8732014106994909.000 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | -132832598551463000675516780904448.000 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 0.000 | ||||
| Minimum | NA | ||||
| Quartile 1 | NA | ||||
| Median | NA | ||||
| Quartile 3 | NA | ||||
| Maximum | NA | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | NA | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | NA | ||||
| Mean of outliers high | NA | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | NA | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||